Cooperatively breeding common marmosets raise their infants with the help of other adult group members, but individual care-taking contribution can vary considerably. We tested four hypotheses that may explain this variation within marmoset family groups. The pay-for-help hypothesis argues that allogrooming is used strategically by parents to pay helpers for helping. The pay-for-infant-access hypothesis claims that helpers use allogrooming as payment for infant-access. The intrinsic predisposition hypothesis suggests that more affiliative individuals are also more motivated for infant-care, and the relationship quality hypothesis that individuals involved in highly affiliative relationships with main caregivers contribute more to infant-care. To test these hypotheses, we followed five marmoset family groups over a total of eight reproductive cycles, and quantified affiliative behavior, infant-carrying, and food sharing over six to 12 weeks around infant-birth. We found no evidence for either the pay-for-help or pay-for-infant-access hypotheses nor did intrinsic prosocial predisposition determine individual infant-care. Mutual dyadic affiliation, however, was positively linked to infant-carrying and food sharing in female and male breeders and in male helpers. This suggests that cooperation during infant-care is mediated by relationship quality rather than strategic grooming in marmosets. Overall, these results may also contribute to a better understanding of cooperation in humans.